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generators(RingOfInvariants) -- the generators for a ring of invariants

Description

This function is provided by the package InvariantRing.

This method gets the algebra generators for a ring of invariants.

i1 : R = QQ[x_1..x_4]

o1 = R

o1 : PolynomialRing
i2 : W = matrix{{0,1,-1,1},{1,0,-1,-1}}

o2 = | 0 1 -1 1  |
     | 1 0 -1 -1 |

              2       4
o2 : Matrix ZZ  <-- ZZ
i3 : T = diagonalAction(W, R)

             * 2
o3 = R <- (QQ )  via 

     | 0 1 -1 1  |
     | 1 0 -1 -1 |

o3 : DiagonalAction
i4 : S = R^T

o4 =     5   3 2   5 3 4     4 2 3     6 3 3   3   2     4 2 2   5 5 5 
     QQ[x x x x , x x x x , x x x x , x x x , x x x x , x x x , x x x ,
         1 2 3 4   1 2 3 4   1 2 3 4   1 3 4   1 2 3 4   1 3 4   1 2 3 
     ------------------------------------------------------------------------
              2
     x x x , x x x ]
      1 2 3   1 3 4

o4 : RingOfInvariants
i5 : gens S

       5   3 2   5 3 4     4 2 3     6 3 3   3   2     4 2 2   5 5 5         
o5 = {x x x x , x x x x , x x x x , x x x , x x x x , x x x , x x x , x x x ,
       1 2 3 4   1 2 3 4   1 2 3 4   1 3 4   1 2 3 4   1 3 4   1 2 3   1 2 3 
     ------------------------------------------------------------------------
      2
     x x x }
      1 3 4

o5 : List

Ways to use this method:


The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/InvariantRing/InvariantsDoc.m2:71:0.